Quantum speed limit and stability of coherent states in quantum gravity

TL;DR

This paper explores the dynamical stability of cosmological coherent states in Loop Quantum Gravity by adapting the Quantum Speed Limit, providing a new method to assess state transitions and stability.

Contribution

It introduces a novel adaptation of the Quantum Speed Limit to quantum gravity and applies it to evaluate the stability of coherent states in Loop Quantum Gravity.

Findings

Coherent states pass the Quantum Speed Limit test for short times.

The developed tools effectively evaluate the variance of the quantum scalar constraint.

The approach offers a new consistency check for stable state proposals.

Abstract

Utilizing the program of expectation values in coherent states and its recently developed algorithmic tools, this letter investigates the dynamical properties of cosmological coherent states for Loop Quantum Gravity. To this end, the Quantum Speed Limit is adapted to Quantum Gravity, yielding necessary consistency checks for any proposal of stable families of states. To showcase the strength of the developed tools, they are applied to a prominent model: the Euclidean part of the quantum scalar constraint. We report the variance of this constraint evaluated on a family of coherent states showing that, for short times, this family passes the Quantum Speed Limit test, allowing the transition from one coherent state to another one.